Joe Biden highlighted the Duke of Edinburgh’s “decades of devoted public service”, Second World War service and environmental efforts in remembering his legacy.
The US president said he and wife Jill were keeping the Queen and her family “in our hearts” as he led international tributes to Philip, who died at the age of 99 on Friday.
“Over the course of his 99-year life, he saw our world change dramatically and repeatedly. From his service during World War II, to his 73 years alongside the Queen, and his entire life in the public eye — Prince Philip gladly dedicated himself to the people of the UK, the Commonwealth, and to his family,” Mr Biden said in a statement.
“The impact of his decades of devoted public service is evident in the worthy causes he lifted up as patron, in the environmental efforts he championed, in the members of the armed forces that he supported, in the young people he inspired, and so much more.
“His legacy will live on not only through his family, but in all the charitable endeavours he shaped.”
Other world leaders also offered their respects, with Irish President Michael D Higgins expressing his condolences to the Queen.
“On behalf of the people of Ireland, I wish to convey my condolences to Her Majesty Queen Elizabeth, her children, her extended family and the people of the United Kingdom,” he said in a statement.
He added: “For over 60 years, and as husband to Britain’s longest serving monarch, Prince Philip served the British people with an unfailing commitment and devotion to duty.”
“In the course of his long service he frequently brought an air of informality to otherwise formal occasions.
“His distinctive presence and unique sense of humour put participants at ease and always engaged those who encountered him.”
President Higgins added the Irish saying “Ar dheis De go raibh a anam dilis”, meaning may his holy soul be on the right side of God.
Barack Obama recounted how he and wife Michelle were apprehensive of the “palaces and pomp” when they visited during his time as US president, but that the Queen and Philip put them “at ease with their grace and generosity”.
“Prince Philip in particular was kind and warm, with a sharp wit and unfailing good humour. It was our first introduction to the man behind the title, and in the years since, our admiration for him has only grown. We will miss him dearly,” Mr Obama added.
His successor Donald Trump said Philip’s death is “an irreplaceable loss for Great Britain, and for all who hold dear our civilisation”.
He said the duke “defined British dignity and grace” and “personified the quiet reserve, stern fortitude, and unbending integrity of the United Kingdom”.
Indian prime minister Narendra Modi recalled Philip’s “distinguished career in the military” and work “at the forefront of many community service initiatives”.
“May his soul rest in peace,” he added.
Along with Mr Modi, other leaders of Commonwealth nations marked the duke’s death.
Australian prime minister Scott Morrison tweeted that he “embodied a generation that we will never see again”.
“Australians send our love and deepest condolences to Her Majesty and all the Royal family.
“The Commonwealth family joins together in sorrow and thanksgiving for the loss and life of Prince Philip. God bless from all here in Australia,” he tweeted.
Canada’s prime minister Justin Trudeau described Philip as a “man of great purpose and conviction” in a tribute posted on the social media platform.
“A man of great purpose and conviction, who was motivated by a sense of duty to others, Prince Philip contributed so much to the social fabric of our country – and the world,” he wrote.
“Prince Philip will be remembered as a decorated naval officer, a dedicated philanthropist, and a constant in the life of Queen Elizabeth II.”
Commonwealth secretary-general Baroness Scotland said like the Queen her “beloved consort” Philip has been “committed” to the Commonwealth.
“So it is heart-breaking that at this moment when we’re in lockdown, when Covid-19 is ravishing the world and all the difficulties, that we should lose an emblem of our unity,” she said.
Outside the Commonwealth, Israel’s prime minister Benjamin Netanyahu said the duke would be “missed in Israel and across the world”.
He wrote on Twitter: “I express my deepest condolences to Her Majesty Queen Elizabeth, Prince Charles, the Royal Family and the people of the United Kingdom on the passing of the Duke of Edinburgh.
“Prince Philip was the consummate public servant and will be much missed in Israel and across the world.”
The Kremlin said Russian President sent the Queen a message to convey his condolences.
“Many important events in the contemporary history of your country are connected with the name of His Royal Highness. He has rightfully enjoyed the respect of the British nation as well as international recognition,” the note said.
And UN Secretary-General Antonio Guterres paid tribute to Philip for “his active work for the betterment of humankind”, his spokesman said.